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Topological phase transitions in the golden string-net model.

Marc Daniel Schulz1, Sébastien Dusuel2, Kai Phillip Schmidt3

  • 1Lehrstuhl für Theoretische Physik I, Technische Universität Dortmund, Otto-Hahn-Straße 4, 44221 Dortmund, Germany and Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France.

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Summary
This summary is machine-generated.

We mapped the phase diagram of a 2D topological model with Fibonacci anyons. Competing interactions reveal quantum critical points separating topological and trivial phases, suggesting new universality classes.

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Area of Science:

  • Condensed Matter Physics
  • Topological Quantum Matter
  • Quantum Information Theory

Background:

  • The Levin-Wen string-net model provides a framework for realizing various topological phases.
  • Fibonacci anyons are key building blocks for non-Abelian topological phases with potential applications in quantum computation.
  • Understanding phase transitions in these models is crucial for their experimental realization and application.

Purpose of the Study:

  • To investigate the zero-temperature phase diagram of the 2D Levin-Wen string-net model with Fibonacci anyons.
  • To identify and characterize the quantum critical points separating topological and nontopological phases under competing interactions.
  • To explore the nature of phase transitions and potential new universality classes.

Main Methods:

  • High-order series expansions around exactly solvable points.
  • Exact diagonalizations of the model Hamiltonian.
  • Accurate computation of quantum critical point positions.
  • Evaluation of critical exponents.

Main Results:

  • The non-Abelian doubled Fibonacci topological phase is identified.
  • This phase is separated from two nontopological phases by second-order quantum critical points.
  • A first-order phase transition occurs between the two nontopological phases at a specific solvable point.
  • Critical exponents suggest the presence of unusual universality classes.

Conclusions:

  • The study provides an accurate phase diagram for the 2D Levin-Wen string-net model with Fibonacci anyons.
  • The findings reveal complex phase transitions driven by competing interactions.
  • The identification of unusual universality classes opens new avenues for research in topological quantum matter.